scholarly journals Flow-Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Long Liu ◽  
Fuzhen Xuan
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Interpolation Formula ◽  
Linear Interpolation ◽  
Flow Induced Vibration ◽  
Precise Integration ◽  
Precise Integration Method ◽  
State Variable ◽  
Fluid Velocities ◽  
Pulsating Fluid

Dynamic analysis of supported pipes conveying pulsating fluid is investigated in Hamiltonian system using precise integration method (PIM). First, symplectic canonical equations of supported pipes are deduced with state variable vectors composed of displacement and momentum. Then, PIM with linear interpolation formula is proposed to solve these equations. Finally, this approach's precision is testified by several numerical examples of pinned-pinned pipes with different fluid velocities and frequencies. The results show that PIM is an efficient and rapid approach for flow-induced dynamic analysis o f supported pipes.

Nonlinear Dynamic Analysis of Low Pressure Rotor of High Parameter Turbine by Improved Segment Direct Integration Method

2014 ◽  
Vol 556-562 ◽  
pp. 1196-1199
Author(s):  
Guang Tian Shi
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Integration Method ◽  
Nonlinear Dynamic Analysis ◽  
Low Pressure ◽  
Computational Accuracy ◽  
Precise Integration ◽  
Nonlinear Part ◽  
Precise Integration Method ◽  
Direct Integration Method

Based on time precise integration method, an improved precise integration method, which called, is studied in the paper to solve the dynamic equation of , where v is an unknown n dimensions vector, Hv and f are respectively the linear homogeneous part and nonlinear part on the right end of equation. Then the calculation expressions of the method are given. The numerical example of nonlinear dynamic analysis of low pressure rotor of high parameter turbine shows that the proposed method is no need to solve the H-1 and the computational accuracy and efficiency can be ensured.

scholarly journals A Modified Precise Integration Method for Long-Time Duration Dynamic Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Ce Huang ◽  
Minghui Fu
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Original Method ◽  
Numerical Dissipation ◽  
Time Duration ◽  
Time Step ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Long Time ◽  
First Time

This paper presents a modified Precise Integration Method (PIM) for long-time duration dynamic analysis. The fundamental solution and loading operator matrices in the first time substep are numerically computed employing a known unconditionally stable method (referred to as original method in this paper). By using efficient recursive algorithms to evaluate these matrices in the first time-step, the same numerical results as those using the original method with small time-step are obtained. The proposed method avoids the need of matrix inversion and numerical quadrature formulae, while the particular solution obtained has the same accuracy as that of the homogeneous solution. Through setting a proper value of the time substep, satisfactory accuracy and numerical dissipation can be achieved.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 334-340 ◽  
Author(s):  
Zhong Wanxie ◽  
F. W. Williams ◽  
P. N. Bennett
Keyword(s):  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Integration Method ◽  
Dynamic Stiffness ◽  
Integration Algorithm ◽  
Precise Integration ◽  
Matrix Computations ◽  
Precise Integration Method ◽  
Count Method ◽  
Mixed Variable

A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation. Therefore the Wittrick-Williams method is extended in this paper to give the eigenvalue count needed by the precise integration method and by other methods involving mixed variable formulations. A simple Timoshenko beam example is included.

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